Well, since I don't think there's a terribly good explanation
here, I will try to add to this node.
By definition, capitalism is an economic system based on private ownership of the means of production. Simple, eh? Well, no... When most people speak of capitalism, they are referring to the idea of laissez-faire (let it be) capitalism. Laissez-faire capitalism refers to the complete separation of the government and the economy. Basically, all aspects of the economy should be controlled by private ownership and the government should stay completely out of it. Capitalism seeks to advance society by the pursuit of self-interest, the basic idea being that as an individual creates more wealth for himself, he is also creating more wealth and opportunities for his fellow men.
In a true capitalist system, the Government is only responsible for protecting the people from violations of their individual rights or fraud. The Government should have no ownership or participation in the economy, and should not regulate businesses. Laissez-faire capitalists also believe that the Government should not have any power to break up or regulate monopolies. They feel that in a truly free market, the only type of monopoly that can exist is an earned monopoly, where the company has created a barrier of entry to competition by being very good at what they do through fair competition. Coercive monopolies are formed due to Government interaction in the marketplace by setting taxes, regulations, or territorial limitations.
In addition, the market would act as a safeguard to itself. There would be no need for any government inspection because any product which was unsafe or poor quality would not succeed in the marketplace. Affirmative action would also not be needed, since it is in the company's best interest to succeed, they will hire the most qualified employees because it is in their best interests. In addition, it would promote a cleaner environment because all land is privately held and polluting would either damage your own property, or violate others rights to private property. Since private industry can do anything cheaper and more efficient than the government, education should also be privately run to allow for completion which would improve the quality of education for all.
This is the theory. As with most economic/social systems, the theory is not the reality. True capitalism has never been tried. In the US, there is a mixture of capitalism and various other ideals. The government has significant power over the economy and actively participates in the economy on a daily basis. Government regulation is abundant, welfare is given out daily, there are government sponsored monopolies, and the government owns land and some means of production.
Of course, one of the definitive modern works on laissez-faire capitalism is Atlas Shrugged by Ayn Rand. It's an excellent book (you can read my short version at that node), however I think if she wanted to write a book about how great capitalism is she should have just come out and done so in a lot fewer words without the out of place fictional love stories and all that. But I digress...
Personally, I think Atlas Shrugged points out several flaws in ideal capitalism. Capitalism is party successful because it encourages greed. We are, inherently, a greedy species. We don't want equality, we want to better ourselves. We want to strive to improve our lives. Capitalism allows this, encourages it even. However, it does not allow for unlimited greed. Capitalism assumes that even though we are greedy, we will play by the rules. This fails under circumstances where people are greedy to the point that they will cheat to get ahead, most often in the form of monopolies. I don't believe that a coercive monopoly is impossible in a truly free market, as there are many things a company can do to create an unfair barrier to entry.
I also think capitalism fails to consider that not everyone is capable of contributing to society equally. The true capitalist view is that if you cannot contribute to society, it is due to laziness and incompetence and thus you don't deserve any of the benefits of society. In reality, there are many people who, due to physical or mental limitations, are not capable of caring for themselves without welfare or the compassion of others. Granted there are many people who abuse this, but there are still those who truly need help through no fault of their own.